Interpreting logistic regression with interaction term

[Brigid Meakin]

Hi,

I was confused at how to first of all write out the interpretation of the logistic regression model. Then when looking at adding an interaction term, how to interpret this too.

My logistic regression looks at whether one invests (Y=1) or not (Y=0).

The explanatory variables included are gender (0=male, 1=female); income (categorical 1/2/3/4), finance module (0 = no finance module, 1 = finance module), year group (categorical 1/2/3/4/5) and freeschool meal (0= no, 1= obtained a freeschool meal)

Running the regression - i input this command:

logit invest1 i.finance1 i.year1 i.income1 i.freeschool1 i.gen1, robust


With these results:

I find that gender is not significant, and only taking a finance module is. My hypothesis is that gender affects the prob of investing. So I have run an interaction model to see whether less females take a finance module:


logit invest1 i.finance1 i.year1 i.income1 i.freeschool1 i.gen1 i.gen1#i.finance1 if (gen1==1), robust


Here are my results:

-------------------------------------------------------------------------------

Please could you help me understand how to interpret these results? I am very stuck trying to put this into words.

Thank you!

[Clyde Schechter]

My hypothesis is that gender affects the prob of investing. So I have run an interaction model to see whether less females take a finance module:

You are contradicting yourself here. These statements are about two different things and require two different models.

The hypothesis that gender affects the probability of investing is already answered in the first regression you ran.

The second sentence about running an interaction model is muddled. An interaction model does not tell you whether fewer females take a finance module. For that you would run a model with taking a finance module as the outcome and gender as a predictor variable. Something like:

logit finance1 i.gen1 // MAYBE OTHER COVARIATES WOULD BE INCLUDED

Instead, you ran an interaction model. But what that tells you is whether the effect of taking a finance module on probability of investing is different in men and women. The interaction term coefficient of -.91 (to 2 decimal places) suggests that it is, and that a finance module has a smaller effect on probability of investment in women than it does in men. The confidence interval does extend slightly into positive territory, but it lies predominantly in the negative. So one might consider the results indeterminate. But unless you chose a sample size specifically to provide adequate power to detect this kind of interaction, you are probably way under-powered to answer this question, so the failure to obtain a "statistically significant" result doesn't really mean much either way. And with N = 105, I'm pretty sure you are, at best, barely powered even for the non-interaction model. The sample size required to adequately power interaction estimation is much, much larger than that required to estimate simple effects.